Conformal Deformation, Monopoles, and Their Application to Control the Measurement, Berry Phase’s Path, and Resonant Frequency of a Spin

The effects of the conformal deformation of physical parameters on the measurement, Berry phase, and resonance of a spin are investigated. We first construct a form-invariant yet measurement-tunable representation of a spinor from the deformed parameter surface. Then, it is shown that the evolution path of the Berry phase is tunable by the conformal index. Third, the source of the path-tunable Berry phase is shown to be the conformal monopole revealed by the recent investigation of the transformation design of quantum states. The dual fields produced by the dual conformal monopole are presented. It is demonstrated that the strengths of the pole and its dual partner are determined by the reciprocally quantized conformal index. Finally, we discuss the influence of the deformation on the resonance of the spin, and show that the resonant frequency follows the quantization rule ω¯R=ωRconformalfactorn/n with ωR as the Rabi frequency without deformation